I assume this kind of slicing isn't possible?

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thats about the worst idea you can have.

resizing by one ... the overhead if you do this over and over again is massive and will cause massive performance lose. (slicing actually has to copy the data manually in case of objects, it even means that it has to do the whole GC involved stuff)
Unless you are sure its only a single attempt, always do resizing on *2 /2 base or similar large (enough free space for further operations) and just ignore the unneeded part until you finished your operations and can be sure that it will remain as it is.

Alternative use Array to TList, add there and cast back ... but that would cast it to common object not to a specific class.